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Omar Khayyám
|caption = |image = |birth_date = 18 May 1048Professor Seyyed Hossein Nasr and Professor Mehdi Aminrazavi. “An Anthology of Philosophy in Persia, Vol. 1: From Zoroaster to ‘Umar Khayyam”, I.B. Tauris in association with The Institute of Ismaili Studies, 2007. |birth_place = Nishapur, Khorasan |death_date =4 December 1131 (aged 82/83) |death_place = Khorasan |religion = Shi'a MuslimYahya Amrajani, Iran p.81 | school_tradition = Persian mathematics, Persian poetry, Persian philosophy |main_interests = Mathematics, Philosophy, Astronomy, Poetry |influences = Abū Rayhān al-Bīrūnī, Avicenna |influenced = Attar of Nishapur | pronunciation = }} (18 May 1048 – 4 December 1131; , ) was a Persian polymath: philosopher, mathematician, astronomer and poet. He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. He also wrote treatises on mechanics, geography, mineralogy, music, and Islamic theology. His significance as a philosopher and teacher, and his few remaining philosophical works, have not received the same attention as his scientific and poetic writings. Al-Zamakhshari referred to him as “the philosopher of the world”. Many sources have testified that he taught for decades the philosophy of Avicenna in Nishapur where Khayyám was born and buried and where his mausoleum today remains a masterpiece of Iranian architecture visited by many people every year.S. H. Nasr Chapter 9. Omar Khayyám died in 1131 and is buried in the Khayyam Garden at the mausoleum of Imamzadeh Mahruq in Nishapur. In 1963 the mausoleum of Omar Khayyam was constructed on the site by Hooshang Seyhoun. Name explanation غیاث ‌الدین Ghiyāth ad-Din - means "the Shoulder of the Faith" and implies the knowledge of Quran. ابوالفتح عمر بن ابراهیم Abu'l-Fat'h 'Umar ibn Ibrāhīm - Abu means father, Fat'h means conqueror, 'Umar means life, Ibrahim is the name of the father. خیام Khayyām - means "tent maker" it is a byname derived from the father's craft. نیشابورﻯ Nīshāpūrī - is the link to his hometown of Nishapur. Early life Ghiyāth ad-Din Abu'l-Fat'h 'Umar ibn Ibrāhīm al-Khayyām Nīshāpūrī ( ) was born in Nishapur, modern-day Iran, but then a Seljuq capital in Khorasan,The Tomb of Omar Khayyâm, George Sarton, Isis, Vol. 29, No. 1 (Jul., 1938), 15.Edward FitzGerald, Rubaiyat of Omar Khayyam, Ed. Christopher Decker, (University of Virginia Press, 1997), xv;"The Saljuq Turks had invaded the province of Khorasan in the 1030s, and the city of Nishapur surrendered to them voluntarily in 1038. Thus Omar Khayyam grew to maturity during the first of the several alien dynasties that would rule Iran until the twentieth century.".Peter Avery and John Heath-Stubbs, The Ruba'iyat of Omar Khayyam, (Penguin Group, 1981), 14;"These dates, 1048-1031, tell us that Khayyam lived when the Saljuq Turkish Sultans were extending and consolidating their power over Persia and when the effects of this power were particularly felt in Nishapur, Khayyam's birthplace.". which rivaled Cairo or Baghdad in cultural prominence in that era. He is thought to have been born into a family of tent-makers (khayyāmī "tent-maker"), which he would make into a play on words later in life: He spent part of his childhood in the town of Balkh (in present-day northern Afghanistan), studying under the well-known scholar Sheikh Muhammad Mansuri. He later studied under Imam Mowaffaq Nishapuri, who was considered one of the greatest teachers of the Khorasan region. Throughout his life Omar Khayyám was tireless in his efforts; by day he would teach Algebra and geometry, in the evening he would attend the Seljuq court as an adviser of Malik-Shah I,Edward FitzGerald, Rubaiyat of Omar Khayyam, xv. and at night he would study Astronomy and complete important aspects of the Jalali calendar. Omar Khayyám's years in Isfahan were very productive ones, but after the death of the Seljuq Sultan Malik-Shah I (presumably by the Assassins sect), the Sultan's widow turned against him as an adviser, and as a result, he soon set out on his Hajj or pilgrimage to Mecca and Medina. He was then allowed to work as a court astrologer, and was permitted to return to Nishapur, where he was renowned for his works, and continued to teach mathematics, astronomy and even medicine. Mathematician Khayyám Sikander was famous during his times as a mathematician. He wrote the influential Treatise on Demonstration of Problems of Algebra (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders. In the Treatise he wrote on the triangular array of binomial coefficients known as Pascal's triangle. In 1077, Khayyám wrote Sharh ma ashkala min musadarat kitab Uqlidis (Explanations of the Difficulties in the Postulates of Euclid) published in English as "On the Difficulties of Euclid's Definitions".The Quatrains of Omar Khayyam E.H. Whinfield Pg 14 An important part of the book is concerned with Euclid's famous parallel postulate, which attracted the interest of Thabit ibn Qurra. Al-Haytham had previously attempted a demonstration of the postulate; Khayyám's attempt was a distinct advance, and his criticisms made their way to Europe, and may have contributed to the eventual development of non-Euclidean geometry. Omar Khayyám created important works on geometry, specifically on the theory of proportions. His notable contemporary mathematicians included Al-Khazini and Abu Hatim al-Muzaffar ibn Ismail al-Isfizari Theory of parallels ]] Khayyám wrote a book entitled Explanations of the difficulties in the postulates in Euclid's Elements. The book consists of several sections on the parallel postulate (Book I), on the Euclidean definition of ratios and the Anthyphairetic ratio (modern continued fractions) (Book II), and on the multiplication of ratios (Book III). The first section is a treatise containing some propositions and lemmas concerning the parallel postulate. It has reached the Western world from a reproduction in a manuscript written in 1387-88 AD by the Persian mathematician Tusi. Tusi mentions explicitly that he re-writes the treatise "in Khayyám's own words" and quotes Khayyám, saying that "they are worth adding to Euclid's Elements (first book) after Proposition 28." This proposition states a condition enough for having two lines in plane parallel to one another. After this proposition follows another, numbered 29, which is converse to the previous one. The proof of Euclid uses the so-called parallel postulate (numbered 5). Objection to the use of parallel postulate and alternative view of proposition 29 have been a major problem in foundation of what is now called non-Euclidean geometry. The treatise of Khayyám can be considered as the first treatment of parallels axiom which is not based on petitio principii but on more intuitive postulate. Khayyám refutes the previous attempts by other Greek and Persian mathematicians to prove the proposition. And he, as Aristotle, refuses the use of motion in geometry and therefore dismisses the different attempt by Ibn Haytham too. In a sense he made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate, . Excerpt: In some sense, his treatment was better than ibn al-Haytham's because he explicitly formulated a new postulate to replace Euclid's rather than have the latter hidden in a new definition. Geometric algebra s.]] This philosophical view of mathematics (see below) has had a significant impact on Khayyám's celebrated approach and method in geometric algebra and in particular in solving cubic equations. In that his solution is not a direct path to a numerical solution and in fact his solutions are not numbers but rather line segments. In this regard Khayyám's work can be considered the first systematic study and the first exact method of solving cubic equations.Mathematical Masterpieces: Further Chronicles by the Explorers, p. 92 In an untitled writing on cubic equations by Khayyám discovered in the 20th century, where the above quote appears, Khayyám works on problems of geometric algebra. First is the problem of "finding a point on a quadrant of a circle such that when a normal is dropped from the point to one of the bounding radii, the ratio of the normal's length to that of the radius equals the ratio of the segments determined by the foot of the normal." Again in solving this problem, he reduces it to another geometric problem: "find a right triangle having the property that the hypotenuse equals the sum of one leg (i.e. side) plus the altitude on the hypotenuse.E. S. Kennedy, Chapter 10 in Cambridge History of Iran (5), p. 665. To solve this geometric problem, he specializes a parameter and reaches the cubic equation x^3+200x=20x^2+2000 . Indeed, he finds a positive root for this equation by intersecting a hyperbola with a circle. This particular geometric solution of cubic equations has been further investigated and extended to degree four equations.A. R. Amir-Moez, Khayyam's Solution of Cubic Equations, Mathematics Magazine, Vol. 35, No. 5 (Nov., 1962), pp. 269-271. This paper contains an extension by the late M. Hashtroodi of Khayyám's method to degree four equations. Regarding more general equations he states that the solution of cubic equations requires the use of conic sections and that it cannot be solved by ruler and compass methods. A proof of this impossibility was plausible only 750 years after Khayyám died. In this paper Khayyám mentions his will to prepare a paper giving full solution to cubic equations: "If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared." This refers to the book Treatise on Demonstrations of Problems of Algebra (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders. Binomial theorem and extraction of roots | width = 25%}} This particular remark of Khayyám and certain propositions found in his Algebra book has made some historians of mathematics believe that Khayyám had indeed a binomial theorem up to any power. The case of power 2 is explicitly stated in Euclid's elements and the case of at most power 3 had been established by Indian mathematicians. Khayyám was the mathematician who noticed the importance of a general binomial theorem. The argument supporting the claim that Khayyám had a general binomial theorem is based on his ability to extract roots.J. L. Coolidge, The Story of the Binomial Theorem, Amer. Math. Monthly, Vol. 56, No. 3 (Mar., 1949), pp. 147-157 Khayyám-Saccheri quadrilateral The Saccheri quadrilateral was first considered by Khayyám in the late 11th century in Book I of Explanations of the Difficulties in the Postulates of Euclid.Boris Abramovich Rozenfelʹd (1988), A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, p. 65. Springer, ISBN 0-387-96458-4. Unlike many commentators on Euclid before and after him (including of course Saccheri), Khayyám was not trying to prove the parallel postulate as such but to derive it from an equivalent postulate he formulated from "the principles of the Philosopher" (Aristotle): :Two convergent straight lines intersect and it is impossible for two convergent straight lines to diverge in the direction in which they converge.Boris A Rosenfeld and Adolf P Youschkevitch (1996), Geometry, p.467 in Roshdi Rashed, Régis Morelon (1996), Encyclopedia of the history of Arabic science, Routledge, ISBN 0-415-12411-5. Khayyám then considered the three cases (right, obtuse, and acute) that the summit angles of a Saccheri quadrilateral can take and after proving a number of theorems about them, he (correctly) refuted the obtuse and acute cases based on his postulate and hence derived the classic postulate of Euclid. It wasn't until 600 years later that Giordano Vitale made an advance on Khayyám in his book Euclide restituo (1680, 1686), when he used the quadrilateral to prove that if three points are equidistant on the base AB and the summit CD, then AB and CD are everywhere equidistant. Saccheri himself based the whole of his long, heroic, and ultimately flawed proof of the parallel postulate around the quadrilateral and its three cases, proving many theorems about its properties along the way. Astronomer }} ]] Like most Persian mathematicians of the period, Khayyám was also an astronomer and achieved fame in that role. In 1073, the Seljuq Sultan Jalal al-Din Malik-Shah Saljuqi (Malik-Shah I, 1072–92), invited Khayyám to build an observatory, along with various other distinguished scientists. According to some accounts, the version of the medieval Iranian calendar in which 2,820 solar years together contain 1,029,983 days (or 683 leap years, for an average year length of 365.24219858156 days) was based on the measurements of Khayyám and his colleagues. Another proposal is that Khayyám's calendar simply contained eight leap years every thirty-three years (for a year length of 365.2424 days).Mapping Time: The Calendar and its History by E.G. Richards (Oxford University Press, 1998) ISBN 0-19-282065-7 , p. 235 In either case, his calendar was more accurate to the mean tropical year than the Gregorian calendar of 500 years later. The modern Iranian calendar is based on his calculations. Heliocentric Theory It is sometimes claimed that Khayyam demonstrated that the earth rotates on its axis by presenting a model of the stars to his contemporary al-Ghazali in a planetarium. Whether or not the story is apocryphal, it would only demonstrate the mathematical equivalence of a rotating earth to rotating spheres, as was well known to Khayyam's immediate predecessors, e.g. al-Biruni, and says nothing about heliocentrism, as a spinning earth can be made entirely consistent with geocentric models. The other source for the claim that Khayyam believed in heliocentrism are Edward Fitzgerald's popular but anachronistic renderingsDonald and Marilynn Olson (1988), 'Zodiac Light, False Dawn, and Omar Khayyam', The Observatory, vol. 108, p. 181-182 of Khayyam's poetry, in which the first lines are mistranslated with a heliocentric image of the Sun flinging "the Stone that puts the Stars to Flight". Calendar Reform Khayyám is claimed to be a member of a panel that introduced several reforms to the Iranian calendar. On March 15, 1079, Sultan Malik Shah accepted this corrected calendar as the official Persian calendar. Here Omar Khayyám is described as "poet and mathematician", i.e. poet appearing first. This calendar was known as the Jalali calendar after the Sultan, and was in force across Greater Iran from the 11th to the 20th centuries. It is the basis of the Iranian calendar which is followed today in Iran and Afghanistan. While the Jalali calendar is more accurate than the Gregorian, it is based on actual solar transit, similar to Hindu calendars, and requires an ephemeris for calculating dates. The lengths of the months can vary between 29 and 31 days depending on the moment when the sun crosses into a new zodiacal area (an attribute common to most Hindu calendars). This meant that seasonal errors were lower than in the Gregorian calendar. The modern-day Iranian calendar standardizes the month lengths based on a reform from 1925, thus minimizing the effect of solar transits. Seasonal errors are somewhat higher than in the Jalali version, but leap years are calculated as before. Poet ruler Malik-Shah I and his contributions to the developments of Mathematics, Astronomy and Philosophy inspired later generations.]] He is believed to have written about a thousand four-line verses or rubaiyat (quatrains). In the English-speaking world, he was introduced through the Rubáiyát of Omar Khayyám which are rather free-wheeling English translations by Edward FitzGerald (1809–1883). Other English translations of parts of the rubáiyát (rubáiyát meaning "quatrains") exist, but FitzGerald's are the most well known. .]] Ironically, FitzGerald's translations reintroduced Khayyám to Iranians "who had long ignored the Neishapouri poet." A 1934 book by one of Iran's most prominent writers, Sadeq Hedayat, Songs of Khayyam, (Taranehha-ye Khayyam) is said to have "shaped the way a generation of Iranians viewed" the poet.Molavi, Afshin, The Soul of Iran, Norton, (2005), p.110 Khayyam's poetry is translated to many languages. Khayyám's personal beliefs are not known with certainty, but much is discernible from his poetic oeuvre. = Views on religion There have been widely divergent views on Khayyám. According to Seyyed Hossein Nasr no other Iranian writer/scholar is viewed in such extremely differing ways. At one end of the spectrum there are nightclubs named after Khayyám, and he is seen as an agnostic hedonist.Sadegh Hedayat pointed out that Khayyám from "his youth to his death remained a materialist, pessimist, agnostic". "Khayyam looked at all religions questions with a skeptical eye", continues Hedayat, "and hated the fanaticism, narrow-mindedness, and the spirit of vengeance of the mullas, the so-called religious scholars". On the other end of the spectrum, he is seen as a mystical Sufi poet influenced by platonic traditions. Era inscription of a poem written by Omar Khayyám at Morića Han in Sarajevo, Bosnia and Herzegovina.]] Seyyed Hossein Nasr, after examining the philosophical works of Khayyám, maintains that it is really reductive to just look at the poems (which are sometimes doubtful) to establish his personal views about God or religion; in fact, he even wrote a treatise entitled "al-Khutbat al-gharrå˘" (The Splendid Sermon) on the praise of God, where he holds orthodox views, agreeing with Avicenna on Divine Unity. In fact, this treatise is not an exception, and S.H. Nasr gives an example where he identified himself as a Sufi, after criticizing different methods of knowing God, preferring the intuition over the rational (opting for the so-called "kashf", or unveiling, method): The same author goes on by giving other philosophical writings which are totally compatible with the religion of Islam, as the al-Risālah fil-wujūd ( , "Treatise on Being"), written in Arabic, which begin with Quranic verses and asserting that all things come from God, and there is an order in these things. In another work, Risālah jawāban li-thalāth masāʾil ( , "Treatise of Response to Three Questions"), he gives a response to question on, for instance, the becoming of the soul post-mortem. S.H. Nasr even gives some poetry where he is perfectly in favor of Islamic orthodoxy, but expressing mystical views (God's goodness, the ephemerical state of this life, ...): :Thou hast said that Thou wilt torment me, :But I shall fear not such a warning. :For where Thou art, there can be no torment, :And where Thou art not, how can such a place exist? :The rotating wheel of heaven within which we wonder, :Is an imaginal lamp of which we have knowledge by similitude. :The sun is the candle and the world the lamp, :We are like forms revolving within it. :A drop of water falls in an ocean wide, :A grain of dust becomes with earth allied; :What doth thy coming, going here denote? :A fly appeared a while, then invisible he became. Considering misunderstandings about Khayyám in the West and elsewhere, Hossein Nasr concludes by saying that if a correct study of the authentic rubaiyat is done, but along with the philosophical works, or even the spiritual biography entitled Sayr wa sulak (Spiritual Wayfaring), we can no longer view the man as a simple hedonistic wine-lover, or even an early skeptic, but a profound mystical thinker and scientist whose works are more important than some verses. C.H.A. Bjerregaard earlier summarised the situation: Abdullah Dougan, a modern Naqshbandi Sufi, provides commentaryAbdullah Dougan Who is the Potter? Gnostic Press 1991 ISBN 0-473-01064-X on the role and contribution of Omar Khayyam to Sufi thought. Dougan says that while Omar is a minor Sufi teacher compared to the giants – Rumi, Attar and Sana’i – one aspect that makes Omar’s work so relevant and accessible is its very human scale as we can feel for him and understand his approach. The argument over the quality of Fitzgerald’s translation of the Rubaiyat has, according to Dougan, diverted attention from a fuller understanding of the deeply esoteric message contained in Omar’s actual material – "Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature". Philosophy in Nishapur, Iran]] Khayyám himself rejects to be associated with the title falsafī "philosopher" in the sense of Aristotelianism and stressed he wishes "to know who I am". In the context of philosophers he was labeled by some of his contemporaries as "detached from divine blessings".Bausani, A., Chapter 3 in Cambridge History of Iran (5), p. 289. It is now established that Khayyám taught for decades the philosophy of Avicena, especially the Book of Healing, in his home town Nishapur, till his death. In an incident he had been requested to comment on a disagreement between Avicena and a philosopher called Abu'l-Barakāt al-Baghdādī who had criticized Avicena strongly. Khayyám is said to have answered "he does not even understand the sense of the words of Avicenna, how can he oppose what he does not know?" Khayyám the philosopher could be understood from two rather distinct sources. One is through his Rubaiyat and the other through his own works in light of the intellectual and social conditions of his time. The latter could be informed by the evaluations of Khayyám's works by scholars and philosophers such as Abul-Fazl Bayhaqi, Nizami Aruzi, and al-Zamakhshari and Sufi poets and writers Attar of Nishapur and Najm-al-Din Razi. As a mathematician, Khayyám has made fundamental contributions to the Philosophy of mathematics especially in the context of Persian Mathematics and Persian philosophy with which most of the other Persian scientists and philosophers such as Avicenna, Abū Rayḥān al-Bīrūnī and Tusi are associated. There are at least three basic mathematical ideas of strong philosophical dimensions that can be associated with Khayyám. # Mathematical order: From where does this order issue, and why does it correspond to the world of nature? His answer is in one of his philosophical "treatises on being". Khayyám's answer is that "the Divine Origin of all existence not only emanates wujud "being", by virtue of which all things gain reality, but It is the source of order that is inseparable from the very act of existence."S. H. Nasr Chapter 9, p . 170-1 # The significance of axioms in geometry and the necessity for the mathematician to rely upon philosophy and hence the importance of the relation of any particular science to prime philosophy. This is the philosophical background to Khayyám's total rejection of any attempt to "prove" the parallel postulate, and in turn his refusal to bring motion into the attempt to prove this postulate, as had Ibn al-Haytham, because Khayyám associated motion with the world of matter, and wanted to keep it away from the purely intelligible and immaterial world of geometry. # Clear distinction made by Khayyám, on the basis of the work of earlier Persian philosophers such as Avicenna, between natural bodies and mathematical bodies. The first is defined as a body that is in the category of substance and that stands by itself, and hence a subject of natural sciences, while the second, called "volume", is of the category of accidents (attributes) that do not subsist by themselves in the external world and hence is the concern of mathematics. Khayyám was very careful to respect the boundaries of each discipline, and criticized ibn al-Haytham in his proof of the parallel postulate precisely because he had broken this rule and had brought a subject belonging to natural philosophy, that is, motion, which belongs to natural bodies, into the domain of geometry, which deals with mathematical bodies. Poetry Omar Khayyám's poems have been translated often and into several languages. Many translators have claimed that their translations of the Rubáiyát of Omar Khayyám are more literal and less controversial than those of Edward Fitzgerald. Recognition Outside Iran and Persian speaking countries, Khayyám has had an impact on literature and societies through the translation of his works and popularization by other scholars. The greatest such impact was in English-speaking countries; the English scholar Thomas Hyde (1636–1703) was the first non-Persian to study him. The most influential of all was Edward FitzGerald (1809–83), who made Khayyám the most famous poet of the East in the West through his celebrated translation and adaptations of Khayyám's rather small number of quatrains ( rubāʿiyāt) in the Rubaiyat of Omar Khayyam.Jos Biegstraaten *A lunar crater was named "Omar Khayyam" after him in 1970. *A minor planet called 3095 Omarkhayyam, discovered by Soviet astronomer Lyudmila Zhuravlyova in 1980, is named after him. See also * Poets of other languages * Persian poetry * Astronomy in medieval Islam * Mathematics in medieval Islam * Nozhat al-Majales * ''Omar Khayyam'' (film) * The Keeper: The Legend of Omar Khayyam References * * * * * * * * * E.G. Browne (1998). Literary History of Persia. (Four volumes, 2,256 pages, and 25 years in the writing). ISBN 0-7007-0406-X * Jan Rypka (1968). History of Iranian Literature. Reidel Publishing Company. . ISBN 90-277-0143-1 * Omar Khayyam: Vierzeiler (Rubāʿīyāt) übersetzt von Friedrich Rosen mit Miniaturen von Hossein Behzad. ISBN 978-3-86931-622-2 Details Notes External links *The Rubaiyat of Omar Khayyam translated by Edward FitzGerald. *Rubaiyat Of Omar Khayyam * (PDF version) ;About *Umar Khayyam, at the Stanford Encyclopedia of Philosophy *Khayyam's works in original Persian at Ganjoor Persian Library *Khayyam in Tarikhema.ir *Listen to The Rubáiyát of Omar Khayyám audiobook at LibriVox *The illustrated Rubáiyát of Omar Khayyám at Internet Archive. *Omar Khayyam's Rubaiyat as translated by Edward Fitzgerald – 1st edition *The Rubaiyat by Omar Khayyam – The Internet Classics Archive *Illustrations to the Rubaiyat by Adelaide Hanscom *Panoramic Images of Khayyam’s Tomb Category:1048 births Category:1131 deaths Category:Philosophers from Nishapur Category:Mathematicians from Nishapur Category:Omar Khayyám Category:Persian poets Category:Medieval Persian astronomers Category:Medieval Persian mathematicians Category:Persian philosophers Category:Persian spiritual writers Category:11th-century mathematicians Category:12th-century mathematicians Category:Medieval writers Category:Astronomers of medieval Islam Category:Mathematicians of medieval Islam Category:12th-century astronomers Category:11th-century poets Category:Persian poets Category:Persian-language poets Category:Poets